Abstract
QU-fitting is a model-fit method to reproduce the model of the Faraday Dispersion Function (FDF or Faraday spectrum), which is a probability distribution function of polarized intensity in Faraday depth space. In order to find the best-fit parameters of the model FDF, we adopt the Markov Chain Monte Carlo (MCMC) algorithm using Geweke’s convergence diagnostics. Akaike and Bayesian Information Criteria (AIC and BIC, respectively) are used to select the best model from several FDF fitting models. In this paper, we investigate the performance of the standard QU-fitting algorithm quantitatively by simulating spectro-polarimetric observations of two Faraday complex sources located along the same Line Of Sight (LOS), varying the gap between two sources in Faraday depth space and their widths, systematically. We fix the frequency bandwidth in 700–1800 MHz and make mock polarized spectra with a high Signal-to-Noise ratio (S/N). We prepare four FDF models for the fitting by changing the number of model parameters and test the correctness of MCMC and AIC/BIC. We find that the combination of MCMC and AIC/BIC works well for parameter estimation and model selection in the cases where the sources have widths smaller than 1/4 Full Width at Half Maximum (FWHM) and a gap larger than one FWHM in Faraday depth space. We note that when two sources have a gap of five FWHM in Faraday depth space, MCMC tends to be trapped in a local maximum likelihood compared to other situations.
Highlights
This is a conference proceeding of “The Power of Faraday Tomography” based on Miyashita et al, 2019 [1].Rotation Measure (RM) synthesis is an advanced technique that enables us to know magnetic fields along a Line Of Sight (LOS) direction using the Faraday Dispersion Function (FDF) (Burn [2]; Brentjens and de Bruyn 2005 [3]; Akahori et al, 2018 [4])
We evaluate the capability of QU-fitting for parameter estimation and model selection through a series of simulations, which consist of preparing fitting models, making mock observation data, and searching for the best-fit parameter set in a given fitting model using Markov Chain Monte Carlo (MCMC)
We examined the functionality of the standard QU-fitting algorithm quantitatively by simulating spectro-polarimetric observations of two extent sources located along the same LOS
Summary
Rotation Measure (RM) synthesis is an advanced technique that enables us to know magnetic fields along a Line Of Sight (LOS) direction using the Faraday Dispersion Function (FDF) (Burn [2]; Brentjens and de Bruyn 2005 [3]; Akahori et al, 2018 [4]). FDF represents the distribution of polarized intensity as a function of Faraday depth, which is proportional to an integration of thermal electron density and magnetic fields along the LOS. Compared with the conventional Faraday rotation technique, FDF gives us three-dimensional information about thermal/cosmic-ray electron densities, polarized sources, and magnetic fields when there is no magnetic field inversion along an LOS. FDF becomes ill-determined, and we cannot distinguish between signal and noise when the observational noise is large. Several techniques have been proposed, for example: RM CLEAN, which removes the sidelobes of the dirty FDF (Hogbom 1974 [5]; Heald et al, 2009 [6]; Kumazaki et al, 2014 [7]; Miyashita et al, 2016 [8]), QU-fitting, which fits model Stokes Q and U parameters to observed Stokes Q, U parameters (O’Sullivan et al, 2012 [9]; Ideguchi et al, 2014,a [10]; Ozawa et al, 2015 [11]; Kaczmarek et al, 2017 [12]; Schnitzeler et al, 2018 [13]; Miyashita et al, 2019 [1]), and compressive sensing, which assumes a sparsity of FDF and optimizes
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